The town's most famous landmark is a ballistic missile incongruously erected in the center of the village green. This was donated in honor of long-time Senator Norris Cotton, a Warren native. The missile was donated by Henry T. Asselin, who brought the missile to Warren from the Redstone Arsenal near Huntsville, Alabama in 1971. The missile is a Redstone, a model which was used to launch a Granite Stater into suborbital flight: Alan Shepard of Derry, New Hampshire, who rode into space aboard MR-3, becoming the first American and the second human in space.
From 1909 until 1970, Glencliff was home to the New Hampshire State Sanatorium, located at an elevation of on the slopes of Mount Moosilauke. Before the discovery of antibiotics, pure mountain air was thought to be curative for patients with tuberculosis. With its own farm on , the facility would treat more than 4,000 individuals over its first half century, admitting between 50 and 100 per year. Many came from the industrial cities of southern New Hampshire such as Concord, Manchester and Nashua. It is now the Glencliff Home for the Elderly.
There were 355 households out of which 28.7% had children under the age of 18 living with them, 51.5% were married couples living together, 9.3% had a female householder with no husband present, and 35.8% were non-families. 28.2% of all households were made up of individuals and 11.0% had someone living alone who was 65 years of age or older. The average household size was 2.46 and the average family size was 2.98.
In the town the population was spread out with 24.5% under the age of 18, 7.2% from 18 to 24, 29.2% from 25 to 44, 25.9% from 45 to 64, and 13.2% who were 65 years of age or older. The median age was 38 years. For every 100 females there were 98.4 males. For every 100 females age 18 and over, there were 97.3 males.
The median income for a household in the town was $34,432, and the median income for a family was $38,125. Males had a median income of $29,625 versus $22,163 for females. The per capita income for the town was $16,454. About 5.1% of families and 10.7% of the population were below the poverty line, including 14.0% of those under age 18 and 7.1% of those age 65 or over.